The pseudo-sequential procedure of [1]}
adapts an online change point detection algorithm to the offline data segmentation problem.
The Isolate-Detect (IDetect) proposed in [2]} operates in a similar vein,
sequentially searching for change points from both ends.
More specifically, it scans \(\mathcal {T}_{s, k, e}(X), \, (s, k, e) \in \mathcal {S}_L(\ell , r) \cup \mathcal {S}_R(\ell , r)\) ,
where \(\mathcal {S}_L(\ell , r)\)  and \(\mathcal {S}_R(\ell , r)\) 
denote the search spaces containing the intervals expanded from the left to the right,
and those expanded from the right to the left, respectively,
for given \(0 \le \ell < r \le n\) , as
\(\mathcal {S}_L(\ell , r) &= \left\lbrace (s, k, e): \, \ell = s < k < e \le r \text{ with } e = m\lambda _n, \, m \in \mathbb {N} \right\rbrace ,\\\mathcal {S}_R(\ell , r) &= \left\lbrace (s, k, e): \, \ell \le s < k < e = r \text{ with } s = n - m\lambda _n, \, m \in \mathbb {N} \right\rbrace ,\) 
